 Hello, and welcome to the session I am Deepika here. Let's discuss a question which says, verifying that the given function is a solution of the corresponding differential equation. x plus y is equal to 10 inverse y, y square into y dash plus y square plus 1 is equal to 0. Now, the given function is a solution of the corresponding differential equation if it satisfies the given differential equation. So, let's have the solution. Now, the given differential equation is y square into y dash plus y square plus 1 is equal to 0. Let us get this equation as number 1 and the given function is x plus y is equal to 10 inverse y. Let us get this equation as number 2. Now, here we observe that equation 1 contains y dash. So, we shall differentiate equation 2 with respect to x to get y dash. So, on differentiating both sides of equation 2 with respect to x we get 1 plus dy by dx is equal to 1 over 1 plus y square into dy by dx. This can be written as 1 plus y dash is equal to 1 over 1 plus y square into y dash or y dash into 1 over 1 plus y square minus 1 is equal to 1, y dash into 1 minus 1 minus y square over 1 plus y square is equal to 1 or y dash into minus y square over 1 plus y square is equal to 1 or y dash is equal to minus 1 plus y square over y square. Now, on substituting the above value of y dash in the given differential equation or in equation 1, we get y square into minus 1 plus y square upon y square plus y square plus 1 is equal to 0. This implies minus 1 minus y square plus y square plus 1 is equal to 0. This implies is equal to 0. Hence, our left hand side is equal to right hand side. Hence, we have seen that the differential equation is satisfied by putting value of y dash derived from the function. Therefore, the given function is the solution of the given differential equation. So, this completes our session. I hope the solution is clear to you and you have enjoyed the session. Bye and take care.